First off, you need to implement INotifyPropertyChanged interface in your view model and raise the PropertyChanged event in the setter of the Rule property. Otherwise no control that binds to the SelectedRule property will “know” when it has been changed.
Then, your XAML
<TextBlock Text="{Binding Path=SelectedRule.Name}" />
is perfectly valid if this TextBlock is outside the ListBox‘s ItemTemplate and has the same DataContext as the ListBox.